I wonder if the following situation has a name. It's come up for me a few times and relies on the fact that a unique solution should exist for each puzzle.There were 4 cells at the corners of a rectangle and 3 had the same pair of possible numbers. The 4th cell had the same pair and one other number. I figured the other number had to be the answer to the 4th cell because otherwise there would be the same pair in the four cells and this would lead to 2 equally valid solutions.Thanks for the input.

Thanks Red Ed for the input. Paul, I wasn't trying to claim credit for an original idea, it was just a question. If a post of mine seems to trivial or stupid to you please feel free to ignore it and don'twaste your time replying.

Well, it depends. That's why this technique is a tiny bit controversial. If the puzzle is well-formed, and only has one unique solution, then the tactic can help you find it, by exploiting that knowledge. But if it was a bad puzzle to begin with, that had more than one solution, then this technique could get you in trouble.

What I'm not sure about, is whether you can get a 2-solutioned puzzle, use this technique (incorrectly, since it's the 'uniqueness' technique, and you don't have a unique solution to exploit) and end up in a position where you have no solutions. But this is a tangent, really. The technique is fine for proper sudoku puzzles.

PaulIQ164 wrote:What I'm not sure about, is whether you can get a 2-solutioned puzzle, use this technique (incorrectly, since it's the 'uniqueness' technique, and you don't have a unique solution to exploit) and end up in a position where you have no solutions. But this is a tangent, really. The technique is fine for proper sudoku puzzles.

I think, that if you for a particular cell place a number that does not appear in that cell in any of the solution grids, you will end up in a contradiction sooner or later. (Example cases are easy to construct). But for proper sudokus the technique works fine.

PaulIQ164 wrote:What I'm not sure about, is whether you can get a 2-solutioned puzzle, use this technique (incorrectly, since it's the 'uniqueness' technique, and you don't have a unique solution to exploit) and end up in a position where you have no solutions.

If you use the uniqueness rule, then you argue that 5 cannot go in r1c1, because if it did the puzzle has two solutions. But 5 cannot go in any other cell, because you either get two 5s in a row or a column. So the uniqueness rule implies no solution. Not using the uniqueness rule there are two solutions.

Edit: The puzzle was wrong when I first posted it, it got mangled somehow. It's now corrected, sorry.

Last edited by Moschopulus on Mon Jan 09, 2006 11:03 am, edited 1 time in total.

I think what people fail to mention is that this technique not merely is restricted to "proper/valid" puzzles, it is restricted to "normal/ordinary" i.e. boring sudoku puzzles. Consider all the other variant forms: killer, diagonal (sudoku X), samurai, overlapping, etc. Almost all other normal sudoku techniques are appliable to these variants, but not this. I've seen numerous users complaint to djape on his X puzzles being with multiple solutions, failing to notice the "X" property. Okay, that's irrelevant... So I guess it's a "pure sudoku" technique...

In fact you can use uniqueness on Killer puzzles, as long as the four numbers being used are restricted to 2 cages (there may be more restrictions I can't fathom out in my head). Also in Samurai and X puzzles under similar limitations. But it's certainly true that it doesn't apply straigt away to variants like other rules do, because, I suppose, the extra restrictions that variants add mean that the underlying 'pure' sudoku involved could have more that one solution (eg, the individual puzzles in a Samurai will have multiple solutions, of which the extra restriction of fitting with the overlapping puzzles will restrics the solver to one).